Problem: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x - 6)^2 - 25$
Solution: The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x - 6)^2 - 25 = 0$ Add $25$ to both sides so we can start isolating $x$ on the left: $ (x - 6)^2 = 25$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x - 6)^2} = \pm \sqrt{25}$ Be sure to consider both positive and negative $5$ , since squaring either one results in $25$ $ x - 6 = \pm 5$ Add $6$ to both sides to isolate $x$ on the left: $ x = 6 \pm 5$ Add and subtract $5$ to find the two possible solutions: $ x = 11 \text{or} x = 1$